domainCost

This module treats recombination redshift as a structural J-cost statement: observationally $z_{\mathrm{rec}}\approx 1100$, and in RS one expects $z_{\mathrm{rec}}=\varphi^k$ with $\log 1100/\log\varphi\approx 14.7$, so the value sits between $\varphi^{14}$ and $\varphi^{15}$.

The cost functional is the unique J forced by the Recognition Composition Law, $J(x)=\frac12(x+x^{-1})-1$ (equivalently $\cosh(\log x)-1$). Upstream copies of Jcost state that it is the recognition cost of a positive ratio and is nonnegative for $x>0$, with a genuine distinction (ratio not one) carrying strictly positive cost.

Here $m$ and $e$ are treated as real parameters whose ratio is fed to that cost; the definition does not yet impose positivity or physical units.

Definitional abbreviation only: expand domainCost m e to Jcost (m / e). No tactics, lemmas, or side conditions. Sibling lemmas (equality at a point, nonnegativity) are expected to unfold this and apply standard J-cost facts.

Gives the local cost scale on which the module’s recombination certificate is built (canonical threshold, Recombin3Cert, and the inhabited cert). It ties mass/energy ratios in cosmology to the same J forced at T5 in the forcing chain and used across gravity and spiral modules.

The parent narrative is structural consistency of $z_{\mathrm{rec}}\approx 1100$ with a $\varphi$-ladder placement between $\varphi^{14}$ and $\varphi^{15}$, not a new dynamical derivation of recombination physics. No downstream edges are recorded yet; the def is infrastructure for the in-module cert chain.